Show/Hide Menu
Hide/Show Apps
Logout
Türkçe
Türkçe
Search
Search
Login
Login
OpenMETU
OpenMETU
About
About
Open Science Policy
Open Science Policy
Open Access Guideline
Open Access Guideline
Postgraduate Thesis Guideline
Postgraduate Thesis Guideline
Communities & Collections
Communities & Collections
Help
Help
Frequently Asked Questions
Frequently Asked Questions
Guides
Guides
Thesis submission
Thesis submission
MS without thesis term project submission
MS without thesis term project submission
Publication submission with DOI
Publication submission with DOI
Publication submission
Publication submission
Supporting Information
Supporting Information
General Information
General Information
Copyright, Embargo and License
Copyright, Embargo and License
Contact us
Contact us
Variational time discretization methods for optimal control problems governed by diffusion-convection-reaction equations
Date
2014-12-15
Author
Akman, Tugba
Karasözen, Bülent
Metadata
Show full item record
This work is licensed under a
Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
.
Item Usage Stats
196
views
0
downloads
Cite This
In this paper, the distributed optimal control problem governed by unsteady diffusion-convection-reaction equation without control constraints is studied. Time discretization is performed by variational discretization using continuous and discontinuous Galerkin methods, while symmetric interior penalty Galerkin with upwinding is used for space discretization. We investigate the commutativity properties of the optimize-then-discretize and discretize-then-optimize approaches for the continuous and discontinuous Galerkin time discretization. A priori error estimates are derived for fully-discrete state, adjoint and control. The numerical results given for convection dominated problems via optimize-then-discretize approach confirm the theoretically observed convergence rates.
Subject Keywords
Optimal control problems
,
Unsteady diffusion-convection-reaction equation
,
Variational time discretization
,
A priori error estimates
URI
https://hdl.handle.net/11511/31155
Journal
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
DOI
https://doi.org/10.1016/j.cam.2014.05.002
Collections
Graduate School of Applied Mathematics, Article
Suggestions
OpenMETU
Core
STREAMLINE UPWIND/PETROV GALERKIN SOLUTION OF OPTIMAL CONTROL PROBLEMS GOVERNED BY TIME DEPENDENT DIFFUSION-CONVECTION-REACTION EQUATIONS
Akman, T.; Karasözen, Bülent; Kanar-Seymen, Z. (2017-01-01)
The streamline upwind/Petrov Galerkin (SUPG) finite element method is studied for distributed optimal control problems governed by unsteady diffusion-convection-reaction equations with control constraints. We derive stability and convergence estimates for fully-discrete state, adjoint and control and discuss the choice of the stabilization parameter by applying backward Euler method in time. We show that by balancing the error terms in the convection dominated regime, optimal convergence rates can be obtain...
A priori error analysis of the upwind symmetric interior penalty Galerkin (SIPG) method for the optimal control problems governed by unsteady convection diffusion equations
AKMAN, Tugba; Yücel, Hamdullah; Karasözen, Bülent (2014-04-01)
In this paper, we analyze the symmetric interior penalty Galerkin (SIPG) for distributed optimal control problems governed by unsteady convection diffusion equations with control constraint bounds. A priori error estimates are derived for the semi- and fully-discrete schemes by using piecewise linear functions. Numerical results are presented, which verify the theoretical results.
Adaptive discontinuous Galerkin approximation of optimal control problems governed by transient convection-diffusion equations
Stoll, Martin; Yücel, Hamdullah; Benner, Peter (2018-01-01)
In this paper, we investigate a posteriori error estimates of a control-constrained optimal control problem governed by a time-dependent convection diffusion equation. The control constraints are handled by using the primal-dual active set algorithm as a semi-smooth Newton method and by adding a Moreau-Yosida-type penalty function to the cost functional. Residual-based error estimators are proposed for both approaches. The derived error estimators are used as error indicators to guide the mesh refinements. ...
Adaptive Symmetric Interior Penalty Galerkin (SIPG) method for optimal control of convection diffusion equations with control constraints
Yücel, Hamdullah; Karasözen, Bülent (2014-01-02)
In this paper, we study a posteriori error estimates of the upwind symmetric interior penalty Galerkin (SIPG) method for the control constrained optimal control problems governed by linear diffusion-convection-reaction partial differential equations. Residual based error estimators are used for the state, the adjoint and the control. An adaptive mesh refinement indicated by a posteriori error estimates is applied. Numerical examples are presented for convection dominated problems to illustrate the theoretic...
Distributed optimal control of time-dependent diffusion-convection-reaction equations using space-time discretization
Seymen, Z. Kanar; Yücel, Hamdullah; Karasözen, Bülent (2014-05-01)
We apply two different strategies for solving unsteady distributed optimal control problems governed by diffusion-convection-reaction equations. In the first approach, the optimality system is transformed into a biharmonic equation in the space time domain. The system is then discretized in space and time simultaneously and solved by an equation-based finite element package, i.e., COMSOL Multiphysics. The second approach is a classical gradient-based optimization method to solve the state and adjoint equati...
Citation Formats
IEEE
ACM
APA
CHICAGO
MLA
BibTeX
T. Akman and B. Karasözen, “Variational time discretization methods for optimal control problems governed by diffusion-convection-reaction equations,”
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
, pp. 41–56, 2014, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/31155.